by Amy B. Williams
Learning Objectives
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Be able to recognize symptoms of ADHD.
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Comprehend the need for behavioral modification to be used in the classroom with an ADHD student.
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Be able to differentiate between positive reinforcement and negative reinforcement.
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Understand the important role of the teacher in making a connection with the ADHD student.
Introduction
It is inevitable in a teacher's career that a student diagnosed with ADHD will be present in their classroom. It will most likely be one of the biggest challenges a teacher can face. They can experience frustration and exhaustion, which will then trickle down to the rest of their students in the classroom. Turning the event of having a student with ADHD into a positive experience, incorporating behavioral modifications, and using classroom techniques will result in success. Success for the teacher, the ADHD student and the entire classroom. Behavior modifications and classroom modifications can be the lifeline for a teacher with an ADHD student, but more importantly, they teach the student very valuable skills to exist within the confines of their diagnosis.
Note
http://www.ed.gov/teachers/needs/speced/adhd/adhd-resource-pt2.pdf
Teaching Children With Attention Deficit Hyperactivity Disorder
Instructional Strategies And Practices
Written by the U.S Department of Education and covers everything from how to identify ADHD, great teacher strategies to classroom seating plans. It is 32 pages full of everything a teacher needs to survive in the classroom!
It's Everywhere, It's Everywhere: Statistical Data and Information
Let's begin by briefly looking into the scientific data to allow for a better understanding of ADHD. ADHD stands for Attention Deficit Hyperactivity Disorder. The American Psychiatric Association defines ADHD as a "persistent pattern of inattention or hyperactivity-impulsivity that is more frequently displayed and more severe than is typically observed in individuals at a comparable level of development" (Diagnostics and Statistical Manual of Mental Disorders, 2000, p. 85). ADD stands for Attention Deficit Disorder and is also a form of ADHD. ADD is not accompanied by hyperactivity (Swanson, 2007). Barkley discusses in his book the staggering toll that ADHD has unleashed on society. He conservatively estimates that 1-2 ADHD students will be present in every classroom in the United States. This breaks down to 2.5 million school-age students that are diagnosed with ADHD or 5-8% of all children attending school (Barkley, 2005). So in every classroom there will most likely be two students diagnosed with ADHD. Teachers are going to have to be proactive by understanding the symptoms of ADHD so let's discuss some a teacher might encounter with an ADHD student.
You're So Smart Now Act Like It: Characteristics of ADHD
Not too uncommon words from a teacher who is frustrated with a student's behavior who they feel is bright and clever, but just can't get to the final stage in a project, sentence or thought. Teachers also witness the impulsive, unorganized, and easily distracted student, along with the fidgety hands, excessive talking, forgetfulness and inability to stay in their seat (Diagnostic and Statistical Manual of Mental Disorders, 2000). In Charles's book, he discusses a hidden meaning behind the inappropriate behavior of a student with ADHD. The hidden meaning is a cry for help saying "reach me and their desire for a connection with their teacher and to be accepted" (Charles, 2008, p. 167). Teachers can look at the glass half-full or half-empty when dealing with a student with ADHD. Making a connection with the student and incorporating behavior and classroom modifications will yield a higher success rate.
Dr. Pavlov, May I Use A Dog Or Two?: Behavior Modification
Two words can sum up the teacher's approach to the ADHD student in the classroom: behavior modification. It will be their life preserver when dealing with the student by using both positive and negative reinforcement. Let's look closer into just what positive and negative reinforcement consists of:
Note
http://www.childdevelopmentinfo.com/learning/teacher.shtml
Classroom Interventions for Children with ADHD
Outstanding website for teachers to use in the classroom that is full of ideas and strategies. It gives different scenarios with appropriate accommodations that should be made.
Don't enter the classroom without it!
Positive Reinforcement
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A touch on the shoulder and a smile so the student knows what good behavior is (Barkley, 2005).
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Ask the ADHD student what types of rewards they enjoy within the first few days of school (Rief, 2007.)
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Tape a piece of paper down on the corner of a desk and as you pass by the student place a sticker on it (Barkley, 2005).
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Place smiley posters up randomly throughout the classroom and stand next to one when the student is making good choices (Barkley,
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2005).
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Use verbal reinforcement with positive praise (Harwell, 2001). An example might be, "How wonderful you raised your hand instead of
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just blurting out the answer Hayden." To change the reward system up a bit, allow special privileges like lunch with the teacher,
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extra time on the computer, and extra recess (Barkley, 2005).
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Use a token system for immediate rewards. In other words, a teacher might want to start with every 2-3 tokens resulting in candy,
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stickers, special classroom duties or free play (Barkley, 2005).
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Give the ADHD student specific tasks (e.g., turning off/on lights, pencil and paper pusher) that will require movement in the
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classroom. Students can also be allowed to move around the room quietly after they complete a task (Nowacek and Mamlin, 2007. An
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example might be, "Hayden, when you are finished with your writing I want you to quietly get up and walk around the classroom for me
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three times while you are keeping your eyes and hands to yourself."
 An example might be, "Alright, I see all but two of my students sitting in
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their chairs and getting ready to go to lunch." This is purposely ignoring the inappropriate behavior, while rewarding the students with
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appropriate behavior.
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Putting a hand on the student's shoulder to remind him or her their behavior is escalating ("Advice for schools..., 2005).
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If the student is destructive or disruptive, the teacher can incorporate a time out system where the student is immediately asked to put away
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their work and place their head on their desk (Barkley, 2005).
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Use a timer that is started when bad behavior is occurring, which is then taken off recess time for the ADHD student (Barkley, 2005).
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Start each day by giving the student 15 minutes of free time to use in the classroom. From that time, the teacher can deduct a minute of free
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time for every instance the student was seen not working or acting inappropriately (Barkley, 2005).
Behavior modification is a useful and positive tool that emphasizes appropriate behavior instead of inappropriate behavior. In addition to behavior modification, there are some other techniques teachers can also incorporate inside the classroom. Let's take a closer look at some of these techniques in the next section.
Tricks Of The Trade: Classroom Modifications
Not only is behavioral modification and reinforcement pivotal in dealing with ADHD students, but just as imperative are classroom modifications. One simply cannot have one without the other. This is really what it is all about: surviving and keeping control of the classroom. Let's take a closer look at the following techniques, which can be used as a cheat sheet for teachers in dealing with ADHD students:
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Provide structure at all times in the classroom and remain calm (Charles, 2008).
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Get eye contact before giving instructions or asking questions (Rief, 2005).
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Stand close to the student to allow for less distraction (Charles, 2008).
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State directions in a logical and ordered sequence (e.g., first, next, last). The teacher should aim for educating the student on how to
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follow rules as quickly as possible without repeating them (Charles, 2008).
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Have the student repeat verbal instructions to ensure he or she clearly understands what is being said (Rief, 2007).
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Provide advanced warning when a change is about to take place (e.g., in five minutes we are going to put away our math work and begin our
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reading). This reduces anxiety and frustration (Rief, 2007).
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Use webbing techniques for writing and graphic organizers, which helps with visual-spatial skills (Harwell, 2007).
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Take five minutes with the student each day to make sure he or she is using a planner for organization (Harwell, 2007).
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Charts and outlines are useful in maintaining attention and understanding concepts (Harwell, 2007).
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Divide tasks into chunks to help decrease frustration and make tasks obtainable (Swanson, 2007). An example might be, "Hayden, we
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will do 15 minutes of writing and 5 minutes of computer."
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Consider shortening assignments if they are too long and overwhelming to the student (Nowacek and Mamlin, 2007).
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Utilize the computer as much as possible with an ADHD student as it will give them immediate feedback (Amen, 2001).
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Give the student encouraging and positive feedback to increase his or her motivation and attention (Rief, 2005).
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Consider how desks are arranged in the classroom and be sure ADHD students are grouped with other non-diagnosed students. Frequently switch
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groups of two students so the ADHD student builds relationships with other students in the classroom. An ADHD student wants nothing more than
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to be accepted by others (Nowacek and Mamlin, 2007).
It's a great idea to have a copy of these techniques handy, even laminated, to reference them quickly when just beginning to teach a student with ADHD.
Note
user.cybrzn.com/kenyonck/add/teaching_tips.html
Teaching Tips For Those Working With ADHD Kids
Dawn Hogan, a 2nd grade teacher from Connecticut, has a fantastic website for teachers. Her first hand experience and knowledge are priceless.
This is a must see!
Final Thoughts
As learned in this article, there is no magic pill or ointment to make the symptoms of ADHD disappear. The teacher needs to be able to face this adversity with a smile, words of support and determination. A deep connection with the ADHD student along with both behavior and classroom modifications are more likely to result in a stimulating and positive educational experience. Teamwork involving teachers, the ADHD student, parents, fellow students and administration is the only way to help combat the diagnosis of ADHD. Students who are ADHD must be taught not just from a book, but they also need to hear they are special and discover that their differences are okay. The success rate for ADHD students depends on the teacher, the teacher's attitude, classroom tips and techniques being used, and their knowledge and comfort level of behavior modification involving
both
positive and negative reinforcements.
Exercise \(\PageIndex{1}\)
1. During the first few days of school, it is imperative that the teacher do which of the following:
A. Let the student know the teacher rules the classroom with an iron fist.
B. Allow the student to choose what rules are best for him or her.
C. Make sure the student knows the teacher would like him or her transferred to another classroom.
D. Discuss with the student what rewards work best for him or her.
2. What two types of approaches are the most effective for teachers when dealing with an ADHD student:
A. Don't be too firm and only give hugs as a reward.
B. Behavior modification and classroom modification.
C. Corporal punishment and expulsion.
D. Discipline
every
misbehavior the student does and not allow any recess.
3. When an ADHD student is completing a task it is best to do the following:
A. Insist he or she must hurry so the teacher can stay on task.
B. Have the teacher divide the task into sub-units or chunks so finality is obtainable.
C. Help the student with the answers because it make the teacher look better to have higher student grades.
D. Tell the other students in the classroom there will be no recess if the ADHD student does not finish in time.
4. Mrs. Williams is the teacher in a classroom with an ADHD student named Hayden. She is trying a new class behavior program
by flipping of green, yellow, and red cards. Which choice best describes Mrs. Williams?
A. Ready to retire and fed up.
B. Utilizing positive reinforcement and appropriate classroom techniques.
C. She is known as the school's yeller and the staff is afraid of approaching her.
D. Begging to get rid of the ADHD student so she can enjoy the rest of the year.
5. Mrs. Williams notices that Hayden has not made a connection with the class and she is concerned. How might she ease him into a group scenario?
A. Pair him with another ADHD student who might better understand his feelings.
B. Allow for more time to pass hoping eventually the class will grow to accept him.
C. Be more flexible with groups and begin to show the class she accepts him and has a connection with him.
D. Talk about the situation with other teachers in the employee lounge.
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Answer
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1. D
2. B
3. B
4. B
5. C
References
"Advice for schools teaching children with ADHD.:
The Practioner
(July 7, 2005): 525. 1-2.
Academic OneFile
. Gale. Lord Fairfax Community College. 27 May 2008.
Amen, Daniel. (2001). Healing ADD: The Breakthrough Program That Allows You To See and Heal the 6 Types of ADD. New York: Berkley Books.
American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision (Washington, DC: American Psychiatric Association, 2000).
Barkley, Russell, A.(2005). Taking Charge of ADHD: The complete, authoritative guide for parents (rev. ed.). New York: Gilford.
Charles, C., M. (2008). Today's Best Classroom Management Strategies: Paths to Positive Discipline. Boston: Pearson Education, Inc.
Harwell, Joan, M. (2007). Complete Learning Disabilities Handbook. San Francisco, CA: Jossey-Bass.
Nowacek, E., Jane, & Mamlin, Nancy. "General education teachers and students with ADHD: what modifications are made?" Preventing School Failure 51.3 (Spring 2007): 28 (8), 11-14.
Academic OneFile
. Gale. Lord Fairfax Community College. 27 May 2008.
http://www.galegroup.com
Rief, Sandra. (2005). How To Reach And Teach Children With ADD/ADHD: Practical Techniques, Strategies, and Interventions. San Francisco, CA: Jossey-Bass.
Swanson, Carl. "Students with ADHD."
Journal of Singing
64.2 (Nov-Dec 2007): 217 (5).
Academic OneFile
. Gale. Lord Fairfax Community College. 27 May 2008, 1-2, 1-8.
http://www.galegroup.com
.
user.cybrzn.com/kenyonck/add/teaching_tips.html. Teaching Tips For Those Working With ADHD Kids.
http://www.childdevelopmentinfo.com/learning/teacher.shtml
. Classroom Interventions For Children With ADHD.
http://www.ed.gov/teachers/needs/speced/adhd/adhd-resource-pt2.pdf
. Teaching Children With Attention Deficit Disorder Hyperactivity Disorder: Instructional Strategies and Practices 2004.


11.8: Works Consulted and Further Reading
Berkhout, Esmé.. 2016. “Tax Battles: The Dangerous Global Race to the Bottom on Corporate Tax,” 46.
Dicken, Peter. 2014. Global Shift: Mapping the Changing Contours of the World Economy. SAGE.
Dorrell, David. 2018. “Using International Content in an Introductory Human Geography Course.” In Curriculum Internationalization and the Future of Education.
Goodwin, Michael, David Bach, and Joel Bakan. 2012. Economix: How and Why Our Economy Works (and Doesn’t Work) in Words and Pictures. New York: Harry N. Abrams.
Grabill, John C. H. 1889. “‘Mills and Mines.’ Part of the Great Homestake Works, Lead City, Dak.” Still image. 1889. //www.loc.gov/pictures/resource/ppmsc.02674.
Gregory, Derek, ed. 2009. The Dictionary of Human Geography. 5th ed. Malden, MA: Blackwell.
Griswold, Daniel. n.d. “Globalization Isn’t Killing Factory Jobs. Trade Is Actually Why Manufacturing Is up 40%.” Latimes.Com. Accessed April 21, 2018. www. latimes.com/opinion/op-ed/la-oe-griswold-globalization-and-trade-help- manufacturing-20160801-snap-story.html.
Howe, Jeff. 2006. “The Rise of Crowdsourcing.” WIRED. 2006. www.wired. com/2006/06/crowds/.
Massey, Doreen B. 1995. Spatial Divisions of Labor: Social Structures and the Geography of Production. Psychology Press.
Rendall, Matthew. 2016. “Industrial Robots Will Replace Manufacturing Jobs — and That’s a Good Thing.” TechCrunch (blog). October 9, 2016. social.techcrunch. com/2016/10/09/industrial-robots-will-replace-manufacturing-jobs-and-thats- a-good-thing/.
Rodrik, Dani. 2015. “Premature Deindustrialization.” Working Paper 20935. National Bureau of Economic Research. doi.org/10.3386/w20935.
Sherman, Len. 2017. “Why Can’t Uber Make Money?” December 14, 2017. https:// www.forbes.com/sites/lensherman/2017/12/14/why-cant-uber-make- money/#2fb5abc10ec1.
Sumner, Andrew. 2005. “Is Foreign Direct Investment Good for the Poor? A Review and Stocktake.” Development in Practice 15 (3–4): 269–85. doi. org/10.1080/09614520500076183.
Zhou, May, and Zhang Yuan. 2017. “Textile Companies Go High Tech in Arkansas - USA - Chinadaily.Com.Cn.” July 25, 2017. usa.chinadaily.com.cn/ world/2017-07/25/content_30244657.htm?utm_campaign=T-shirt%20line&utm_source=hs_email&utm_medium=email&utm_content=54911122&_ hsenc=p2ANqtz-9WyxMiFliVTrpO35Quk5KN0XpHHHj2bYn9-7WKp3Tt_ iF8LUsO9Q6m6OEH892iW9QcXJ4kvAk8C1Ooiy5TffzH6URrPVnKTrvZ3 TEFQ_zyt6rIjp0&_hsmi=54911122.


4.2: Building Blocks of a Theory
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David Whetten (1989) suggests that there are four building blocks of a theory: constructs, propositions, logic, and boundary conditions/assumptions. Constructs capture the “what” of theories (i.e., what concepts are important for explaining a phenomenon), propositions capture the “how” (i.e., how are these concepts related to each other), logic represents the “why” (i.e., why are these concepts related), and boundary conditions/assumptions examines the “who, when, and where” (i.e., under what circumstances will these concepts and relationships work). Though constructs and propositions were previously discussed in Chapter 2, we describe them again here for the sake of completeness.
Constructs are abstract concepts specified at a high level of abstraction that are chosen specifically to explain the phenomenon of interest. Recall from Chapter 2 that constructs may be unidimensional (i.e., embody a single concept), such as weight or age, or multi-dimensional (i.e., embody multiple underlying concepts), such as personality or culture. While some constructs, such as age, education, and firm size, are easy to understand, others, such as creativity, prejudice, and organizational agility, may be more complex and abstruse, and still others such as trust, attitude, and learning, may represent temporal tendencies rather than steady states. Nevertheless, all constructs must have clear and unambiguous operational definition that should specify exactly how the construct will be measured and at what level of analysis (individual, group, organizational, etc.). Measurable representations of abstract constructs are called variables . For instance, intelligence quotient (IQ score) is a variable that is purported to measure an abstract construct called intelligence. As noted earlier, scientific research proceeds along two planes: a theoretical plane and an empirical plane. Constructs are conceptualized at the theoretical plane, while variables are operationalized and measured at the empirical (observational) plane. Furthermore, variables may be independent, dependent, mediating, or moderating, as discussed in Chapter 2. The distinction between constructs (conceptualized at the theoretical level) and variables (measured at the empirical level) is shown in Figure 4.1.
Propositions are associations postulated between constructs based on deductive logic. Propositions are stated in declarative form and should ideally indicate a cause-effect relationship (e.g., if X occurs, then Y will follow). Note that propositions may be conjectural but MUST be testable, and should be rejected if they are not supported by empirical observations. However, like constructs, propositions are stated at the theoretical level, and they can only be tested by examining the corresponding relationship between measurable variables of those constructs. The empirical formulation of propositions, stated as relationships between variables, is called hypotheses . The distinction between propositions (formulated at the theoretical level) and hypotheses (tested at the empirical level) is depicted in Figure 4.1.
The third building block of a theory is the logic that provides the basis for justifying the propositions as postulated. Logic acts like a “glue” that connects the theoretical constructs and provides meaning and relevance to the relationships between these constructs. Logic also represents the “explanation” that lies at the core of a theory. Without logic, propositions will be ad hoc, arbitrary, and meaningless, and cannot be tied into a cohesive “system of propositions” that is the heart of any theory.
Finally, all theories are constrained by assumptions about values, time, and space, and boundary conditions that govern where the theory can be applied and where it cannot be applied. For example, many economic theories assume that human beings are rational (or boundedly rational) and employ utility maximization based on cost and benefit expectations as a way of understand human behavior. In contrast, political science theories assume that people are more political than rational, and try to position themselves in their professional or personal environment in a way that maximizes their power and control over others. Given the nature of their underlying assumptions, economic and political theories are not directly comparable, and researchers should not use economic theories if their objective is to understand the power structure or its evolution in a organization. Likewise, theories may have implicit cultural assumptions (e.g., whether they apply to individualistic or collective cultures), temporal assumptions (e.g., whether they apply to early stages or later stages of human behavior), and spatial assumptions (e.g., whether they apply to certain localities but not to others). If a theory is to be properly used or tested, all of its implicit assumptions that form the boundaries of that theory must be properly understood. Unfortunately, theorists rarely state their implicit assumptions clearly, which leads to frequent misapplications of theories to problem situations in research.


2.9: Korea, Japan, and Southeast Asia
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Learning Objectives
By the end of this section, you will be able to:
- Discuss how geography and climate change influenced the early history of Korea , Japan , and Southeast Asia
- Describe the cultural exchanges between ancient Korea and Japan
- Compare daily life in ancient Korea, Japan, and Southeast Asia
Korea, Japan, and Southeast Asia were notable in the ancient world as homes to cultures uniquely engaged with the wider world. Via trade, religion, and diplomacy, Korea and Japan borrowed and adapted from Chinese civilization, but even more importantly from each other. Ties between Southeast Asia and India likewise proved formative in the eras in which many cultures evolved from small cities and agrarian villages into trade-post empires with monumental architecture. Conversely, geography, climate, and the early cultural forms produced by the first migrants meant that each area also produced its own indigenous systems. For example, Buddhist missionaries traveled from the Indian subcontinent across the Silk Roads and pilgrims trekked to temples to study and eventually bring home tools to convert their native cultures, but in each destination the faith was transformed into hundreds of new sects and interpretations of the path to enlightenment.
Ancient Korea
The earliest humans to reach the Korean peninsula did so around thirty thousand years ago. The land is very hilly, and mountains in the north form a barrier with Manchuria. Important rivers include the Daedong, the Han, and the Yalu. Winters are cold and snowy in the north, while summer months in the south feature blistering heat and torrential rains. Archaeologists have found evidence of bronze weapons dating back to 1300 BCE, but no clear proof that Korea at that time produced a Bronze Age civilization. The earliest written records of the first Koreans come from China, where the Book of Documents recounts the creation of a fief known as Joseon , located in northern Korea and awarded to a Chinese noble referred to as Gija . Later records in Chinese documents from 200 BCE to 313 CE provide descriptions of various small states in areas of Korea and Manchuria.
Seen from the vantage point of Chinese authors, our picture of ancient Korea begins to take shape during China’s Han dynasty, when the peninsula was home to a number of small tribes, cultures, and communities living near the borders of the Chinese empire. From these Chinese records it is also clear that the earliest Koreans were in constant contact and exchange with not just the Chinese but also Inner Asian Steppe peoples like the Xiongnu as well as settlers in Japan . Thus, ethnicity in ancient Korea was quite fluid and prone to change. Groups borrowed liberally from each other’s cultures, traded, and were absorbed and transformed by conquest.
The transformation of Korea into a unified culture and civilization is a story with many stops and starts. Historians often begin with the narrative of the Han dynasty historian Sima Qian , which tells of the dynasty’s efforts to suppress the Xiongnu by invading northern Korea and establishing four garrisons there, from the Liao River to near today’s Seoul. The presence of Chinese generals, troops, and settlers spurred exchange with societies on the Korean peninsula, which borrowed from Chinese culture the ideas of coins, seals, artwork, and building techniques to make roads and mounded tombs. Adopted by tribal chieftains and aristocratic warrior families, Chinese culture provided a wealth of material needed to engineer the first Korean states by controlling large areas of the northern half of the peninsula.
When unable to trade, Korean tribal societies mimicked the Xiongnu and raided the Chinese settlements, drawing strength and forging their own war bands. Among the early Korean polities noted in Chinese records in the north were Joseon, Goguryeo , and Buyeo , a frequent ally of the Han. With the collapse of the Han , each of these Korean societies lost a valuable partner and source of weapons, technology, and wealth. In the fourth and fifth centuries CE, all three struggled to defend themselves against rising powers in the north, such as the Xianbei .
In roughly the same time frame, in the central and southern parts of the Korean Peninsula, and therefore beyond the reach of Chinese administration, three groups known collectively as the Three Han established their territories. Chinese sources from the time refer to people in the southwest as the Mahan , those in the southeast as Jinhan , and between them a group known as the Byeonhan . These societies were ruled by aristocratic families that chose a chief and controlled the lives of lower-ranking commoners, servants, and enslaved people.
The Three Han were far less formidable military powers than their counterparts to the north, in part because they lacked horses and fought primarily on foot. On the other hand, they showed considerable cultural fluidity and knowledge of their neighbors. In Jinhan, many tattooed their bodies in decorative patterns like those found on the bodies of the Wa living in Japan, not surprising given that groups moved relatively freely between Japan and Korea in this age. Residents of Korea traveled to Japan, sometimes as traders and fishers and other times as migrants and permanent settlers. In Mahan, clothing and hairstyles mimicked a style used by the Xianbei on the Inner Asian Steppe, even as their lifestyles revolved around farming rather than a nomadic culture lived on horseback. Indeed, it appears that early Korean societies were quite selective in their borrowing.
Practices such as the levirate , in which a young male marries his elder brother’s widow, were used widely by Inner Asian Steppe peoples and adopted by a number of early Korean ruling families. But the decision whether to emulate the Chinese, Japanese, or other neighbors presented a range of options and cultural choices for chieftains and elite families to build on in this age.
The decline of Chinese power in the fourth century unleashed a wave of refugees that proved pivotal in speeding up the process of state-building in Korea, opening an age known as the Three Kingdoms (313–668 CE). The three kingdoms in questions were Goguryeo , Baekje , and Silla (Figure 5.11). Chinese immigrants resettling within the bounds of Korea provided a source of knowledge about political practices that strengthened the rule of elites, transforming them into kings. These kings commanded large armies, drawing legitimacy from their military prowess and creating mounded tombs that required vast resources and labor. From the struggles against groups such as the Khitan and Xianbei in the north emerged the kingdom of Goguryeo. In the late fourth century, under the leadership of King Gwanggaeto , this kingdom drove southward in a series of expansionist wars against its main rival, the Korean kingdom of Baekje and its allies from Japan, the Wa. In doing so, Goguryeo managed to make the third of the Three Kingdoms, Silla, a vassal by the early fifth century.
Beyond Goguryeo’s militarism, its expansion was marked by two other critical developments. The first was its skillful use of diplomacy and regional politics to manage alliances and threats, playing off groups within and around the Korean peninsula to secure its power. The second was the adoption of a written script from China, evidenced by 414 CE in a stone slab inscribed to note the accomplishments of King Gwanggaeto upon his death. Goguryeo’s elites also learned from the Chinese the art of adorning their large, mounded tombs with colorful murals depicting the lives of royals surrounded by dancers, servants, and enslaved people. Images of large battles, wrestling matches, and mythical creatures such as the phoenix in other mural scenes suggest the emergence of a rich courtly life.
During the Three Kingdoms era, the Chinese writing system spread throughout Korea, allowing those excluded from the ranks of aristocratic families a chance to seek appointment as scribes. The literacy necessary to study Confucian texts or Buddhist sutras, teachings of the Buddha, was a rare and very valuable skill. Knowledge of Chinese culture was another means to a life within the Korean courts, especially when writing poetry became a favorite pastime of Korean royalty and composing an eloquent verse was a critical sign of nobility and refinement. Many kingdoms sent royals, aristocrats, traders, scholars, and monks to China as apprentices to acquire skills and expertise they could bring home. These groups had an indelible impact on early Korean culture and society, particularly as Buddhism developed and grew into distinct sects and traditions. A few Korean Buddhist monks even traveled as far as India and central Asia, while others worked as teachers in the Three Kingdoms, inspiring new forms of painting, sculpture, and jewelry, and later the famed Buddhist monument, the first-century Seokguram Grotto (Figure 5.12).
These changes to the Korean political, social, and spiritual landscape also powered Gogoryeo’s rival state Baekje . The kingdom of Baekje emerged from its home near the Liao River in Manchuria to conquer and absorb the Mahan territory in 369. To consolidate their control over the southwestern area of the peninsula, Baekje’s rulers created a Chinese-style bureaucracy with a chief minister and carried on a successful maritime trade with China and Japan . Demand for Chinese culture, weapons, and Buddhism gave Baekje influence and prestige in Japan. However, a military defeat by Goguryeo and Silla in 475 kept Baekje hemmed in below the Han River. Afterward, Baekje turned its energy to upsetting the balance of power on the Korean peninsula by entreating Silla to rise against Goguryeo, its protector and overlord.
Ultimately, however, it was Silla that emerged from these plots to unify a larger share of today’s Korea than any kingdom that preceded it. The smallest kingdom at the beginning of the era, located in the southeastern corner of the peninsula, Silla was ruled by powerful families that, like their neighbors, eventually copied models from China to wield power. Silla’s rulers created Chinese-style ministries and codes of law and supported the practice of Buddhism to enhance their prestige and legitimacy. Maritime trade later proved a channel for Silla to form an alliance with a reunified China under the Sui and then the Tang dynasties. Conflict between Goguryeo and the Sui began in the 590s and lasted for decades. Later, the Tang supplanted the Sui and renewed Chinese ambitions to dominate the Korean peninsula.
By the 640s, the skillful diplomacy of Queen Seondeok of Silla (Figure 5.13) had leveraged the hostility between Goguryeo and the Chinese into the means for a Silla alliance with the Tang. Her kingdom’s ships proved invaluable in ferrying Chinese armies onto the peninsula to lay conquest. Together, Silla and the Tang first subjugated Baekje and then eliminated Goguryeo in the north. Then, while the Tang set up bureaucracies to administer Korea , Seondeok’s successors in Silla conspired with the defeated forces of their rivals to evict the invaders. Together, the remnants of the Baekje and Goguryeo’s armies under the sway of Silla expelled Chinese forces in 676, ushering in a new era of unified rule over much of the peninsula that lasted from 668 to 892 CE. For a time, Silla severed its relations with the Tang, forgoing a critical resource that had powered its survival for centuries. But by the eighth century, new threats to both the Tang and Silla had emerged in the north. As a result, Silla once again sent tribute to the Chinese in return for protection and trade.
Part of Queen Seondeok’s legacy was a period of unprecedented female rule, during which new art forms emerged that in later centuries became distinctive Korean traditions. In ancient Korea, women wielded power as royal princesses, and affluent women often served as advisors and regents. But Queen Seondeok’s reign paved the way for future queens of Silla, Jindeok , and Jinseong , to inherit the throne. Over time, Korean artisans learned from China how to make celadon ceramic, known for its lustrous green glaze, creating exquisite vases, jugs, bowls, and even pillows with Buddhist motifs such as cranes and clouds. In later centuries these works helped support a robust trade network running from China through Korea to Japan.
Beyond the Book
The Tombs of Goguryeo
Chinese rulers were not the only ones to build tombs that provide us with clues about what they valued in life. The rulers of the Korean kingdom of Goguryeo also constructed tombs decorated with murals depicting everyday scenes, presumably representing the lives they had lived and the lives they hoped to have after death. Shown here (Figure 5.14) are murals from the tomb of a Goguryeo man who was buried in the fourth century CE, not long after the end of China’s Qin dynasty. As you study the images, consider what they tell us about life among the Goguryeo elite at this time.
- What do these murals tell you about the lives of Goguryeo’s elite? What did they value and what were their concerns?
- Do you see any Chinese influences in these depictions? If so, where are they?
Ancient Japan
As in Korea, geography shaped much of Japan ’s early development and history. Four main islands make up Japan. The northernmost is Hokkaido . Then comes Honshu , which is home to Tokyo and the largest present-day population. Continuing south, the next island is Shikoku , and finally Kyushu , which is closest to the Asian mainland. Japan today also includes the islands of Okinawa and thousands of others strewn across the Pacific. But much of the story of ancient Japan concerns only the main isles, the inland Sea of Japan, the country’s countless mountains, and a few fertile plains fed by monsoon rains that sustain agriculture.
Critical to the formation of the main islands and their geographical features is the belt known as the Ring of Fire (Figure 5.15), mapped by a horseshoe-shaped line drawn around the rim of the Pacific Ocean to mark a zone of frequent earthquake and volcanic activity that has generated countless tsunamis in Japan’s distant past and modern day.
The story of prehistoric Japan is typically divided into two halves: the era of Jōmon hunters, ranging from 14,500 to 300 BCE, and that of the Yayoi agriculturalists who emerged after them to dominate the centuries from 300 BCE to 300 CE. These groups had no concept of themselves as “Japanese” in a sense recognizable to us today. But they left their imprint on the main isles via migration, settlement, and the development of practices for making the fertile plains, mountainous forests, and innumerable ocean bays and rivers their homes. Without written records, our knowledge of the Jōmon and Yaoyi is almost wholly based on the archaeological evidence and contemporary theories about the pathways humanity followed out of Africa and across the world. Early hominids likely made their way to the Japanese archipelago when it was still connected to the Asian continent, perhaps over 100,000 years ago. Hunting giant mammals such as elephants, wolves, and enormous deer, many of these early hunters moved to an area near today’s Sea of Japan. Much later, changing climates led ocean levels to slowly rise and cover the stretches of land that connected Japan to the Asian mainland.
Linguists theorize that ultimately three early waves of foragers and hunters made their way overland or across the Tsushima Strait that separates the four main isles from the Asian mainland. These groups were descended from Ural-Altaic, Chinese, and Austro-Asiatic peoples. The climate shift that severed Japan from the Asian continent around twelve thousand years ago transformed the newly formed isles and the game these people once hunted. Grasslands for bison disappeared, for example, and wolves became smaller.
But the early inhabitants adapted, inventing new technologies to enhance their chances for survival. In the caves of Kyushu, archaeologists have found evidence of one of the world’s earliest technological breakthroughs, the development of pottery . Known for its elaborate handles and distinctive cord patterns around rims, this pottery allowed Japan’s inhabitants to become more sedentary and less dependent on finding wild game and foraging for edible plants. First used to store vegetables and boil water from the sea to make salt, the pottery called Jōmon was likely later used for rituals to promote unity and cooperation (Figure 5.16). The increasingly sophisticated culture of the people, also called Jōmon, was characterized by settlements with shared spaces for burials, food storage, and elaborate ceremonies. Among the important cultural symbols were earthenware figurines known as dogu .
Skeletal remains of the Jōmon people suggest that despite their diverse diet of fruits, nuts, and seafood such as clams and fish, they lived with the constant threat of starvation and malnutrition. Another shift in the region’s climate produced a deadly drop in temperatures that led to a decline in the populations of game such as deer and boar. To survive, many Jōmon moved to the coastal areas to supplement their food supply by fishing. Others likely began experimenting with early forms of agriculture; evidence suggests the cultivation of yams and lily-bulbs in the years from 3000 to 2400 BCE. Further evidence of early agriculture comes from traces of rice found in jars dated to the later years of the Jōmon era.
Agriculture and the Yayoi
The next phase of Japan’s prehistory is marked by the leap into agriculture and is known by the name of a separate people and culture, the Yayoi . Beginning in 300 BCE, a new wave of migrants descended from groups in northern Asia began arriving on the southern island of Kyushu . They brought with them knowledge about cultivating barley, buckwheat, and later rice, and gradually they overwhelmed and replaced the Jōmon. Later, the Yayoi built impressive storehouses for grain and domesticated horses and dogs. Other archaeological sites show that, as Yayoi culture spread, the people developed the capacity to engineer the landscape for farming by creating irrigation canals, wells, and pits. Agriculture brought stability and growth, and the Yayoi population is estimated to have ballooned to more than half a million people by the first centuries of the common era.
The Yayoi period marked a turning point in Japan’s prehistory. From this point forward, Korea, China, and Japan were in more consistent contact than in the centuries before. This was especially the case because in the Bronze Age , with copper in short supply on the islands of Japan, the Yayoi were forced to import much of the material. The Yayoi period also marked the beginning of a written record of Japan.
Han conquests and the construction of garrisons on the Korean peninsula began a period of trade in bronze mirrors, iron weapons, and agricultural practices transmitted via Korea to Japan. The Han dynasty (206 BCE–220 CE) and later the kingdom of Cao Wei (220–265 CE) also sent occasional envoys to Japan (which the Han called the Wa kingdom). These envoys left behind the first written records of the lives and cultures of the Yayoi. Their observations show a slow but gradual transformation of society and politics. Despite increasing food surpluses and material abundance, the Yayoi people at first remained largely communal, sharing wooden tools and public spaces. Over time, the appeal of certain areas and sites for agriculture led to competition and increasing warfare and, by extension, the emergence of states to provide for defense.
Chinese records also note the distinctive style of dual governance—in which power was shared between male and female rulers—that developed in early Japanese states at the end of the Yayoi era. Among the notable rulers was Queen Himiko , who ruled in the early third century and, in return for paying tribute to the Chinese emperor, was recognized as an ally and given a golden seal. Ruling alongside Himiko was her younger brother, who handled the administration of her realm. The Cao Wei’s records show that Himiko was at war with a neighboring king and staked the legitimacy of her rule on her spiritual powers, expressed in elaborate burials, the practice of divination, and other sacred rituals. Through such specialization, ancient Japanese women exercised political power and influence, possibly built upon the legacy of the Jōmon, whose dogu figurines depicted women as deities ensuring fertility and safety.
Chinese envoys noted that Japan was also home to an increasingly stratified society that included aristocratic families, merchants, skilled divers and fishers, farmers, and other commoners. With warfare constant, palaces looked more like garrisons, but granaries and markets were full and lively. And while these early Japanese lacked a written script, the Yayoi did develop a rich art form literally written on their bodies, as the practice of tattooing patterns to denote rank, status, and family was widespread in this era.
The Dawn of the Yamato Age
Records of Queen Himiko’s era also suggest a growing concentration of political power and control over territories held by a loose confederation of states and powerful families. This period, known as the Yamato era , was marked by the construction of tombs for deceased royals like Himiko, who were buried with an impressive array of treasures and human sacrifices to accompany them in the afterlife.
It may be that the onset of the Yamato era was produced by a changing climate and constant turmoil in Japan, as a result of which many of the island’s inhabitants despaired and abandoned deities who seemed negligent in their duty to protect them. Instead, new gods associated with an imported technology—mirrors from China and Korea—arose to take their place. Powerful rulers and a new military class forged from warfare associated themselves with these new gods, or more importantly, with the female god of the Sun, Amaterasu , who soon became the ancestral figurehead of the imperial household. Yamato kings further accrued power by brokering alliances, managing trade, giving symbolic gifts, and presiding over ceremonies designed to forge a common culture across Japan.
As co-rulers of a kingdom or heads of households, women continued to wield political clout by using expertise in sorcery via items such as mirrors and often expressing their triumphs in gold jewelry and earrings. Many spiritual practices were imported from earlier Chinese dynasties such as the Shang dynasty. For example, during the burial of Queen Himiko, Chinese envoys recorded that Japanese employed the art of divining the future with heated bones by reading their cracks to foretell the outcome of harvests and wars. Other burial practices such as water purification were more indigenous to Japan and left an imprint on later religions such as Shintoism . Later, new foreign religions such as Buddhism were used by women such as Empress Suiko , who ruled in the early seventh century CE and sought to preserve women’s role in politics through practices such as piety, rigorous study of sutras, and the construction of shrines and temples.
Regardless, it was the construction of large keyhole-style tombs and control over the burial rituals that brought the Yamato rulers power over the area stretching from western Honshu to northern Kyushu. Employing laborers and skilled artisans such as blacksmiths, the Yamato tomb makers showed their wealth and organizational capacity, skills they used later to create capital cities with large markets and highways to the countryside and the coastal ports. To centralize power, kings soon began issuing law codes, such as Prince Shotoku’s Seventeen Article Constitution in 604. The emphasis on law as the basis for rule, the creation of a bureaucracy to help rulers govern, and Confucian values embedded in the document show the Yamato’s reliance on Chinese culture as a source of ideas and inspiration. Borrowing from the Chinese model for imperial statecraft, the Yamato strengthened their rule with mythology and bejeweled regalia, elevating kings to godlike status and eventually transforming them into emperors. Later legal codes such as the Kiyomihara Codes in 689 organized monasteries, created a judiciary, and managed relations between the king’s advisors and vassals. These set the stage for the evolution of Japan’s culture and political system in the later Heian and Nara periods.
Link to Learning
Prince Shotoku’s “Seventeen Article Constitution” was an effort to reform the Japanese state along the lines of the Chinese imperial model. Read the translated law codes at Columbia University’s Asia for Educators site.
To the north, beyond the lands of the Yamato, was another group descended from the early Jōmon foragers who had lived on and resisted the sweep of Yayoi settled agriculture. Later, they continued to forage and hunt and practice their own spiritual beliefs, rejecting the Yamato cultural sphere and its borrowings from China, such as Buddhism, Confucianism , and the idea of large states governed by kings and emperors. While the later Japanese imperial courts in Nara and Heian deepened ties with China’s Tang dynasty, these northern people existed in another orbit defined by contact with smaller northern Asian cultures, such as the Satsumon people of Hokkaido. Relations with the descendants of the Yamato to the south soured over these centuries, as Nara and Heian came to call the northerners Emishi , or “barbarians.” The Emishi survived from the seventh to the eleventh century despite repeated attempts by emperors and militarists from the south to subjugate them. They resisted via war, moved to remote areas, and used other forms of evasion, but the culture of Japan’s south moved inexorably north, and the smaller remnants of the Emishi were subdued by the end of the ninth century.
Southeast Asia
The term “ Southeast Asia ” describes a large area in subtropical Asia that can also include thousands of islands in the Pacific. Today it often refers to Brunei, Burma, Thailand, Laos, Cambodia, Vietnam, Malaysia, Singapore, and Indonesia. For much of human history, travel across this area was far easier by boat along the shore and between islands than overland. Lands were more sparsely populated than in India, China, Japan, and Korea, and most communities were isolated from their closest neighbors by forests and mountains. Early on, however, they became able to engage with other peoples through the sea lanes.
In general, communities in Southeast Asia settled first along coastlines near rivers, lakes, and the oceans and seas. But archaeological sites in Thailand, Burma, and Laos prove that many chose to make upland regions their homes as well. As in India, early agriculture was driven by the rhythms of monsoon season. Farmers developed rainwater tanks to manage their supply of water and learned how to grow rice in paddies. A reliance on slash-and-burn agriculture meant that many Southeast Asians had to migrate after the soil had been exhausted, making the population fluid as people moved from one area to the next. The social structure, too, was less stratified than in India and China. Only with the later arrival of new religions such as Buddhism and Hinduism did priestly and kingly classes start to form and play a central role in religion and politics.
Despite its great territorial expanse and varying climates and topography, the region does have broad commonalities that make it useful to see Southeast Asia as one geographic and cultural zone (Figure 5.17). For example, its location between India and China led to the growth of royal courts that borrowed from foreign traditions to develop rituals and diplomatic relations, assert control over ordinary farmers and fishers, and create trading-post empires. The region’s geography and climate also made sailing a universally efficient craft. For centuries, merchants and adventurers traveling from the Indian landmass along the coastlines of Asia have exploited monsoon winds from June to November that easily push boats all the way to the Malaysian peninsula. Return voyages were made possible by a second set of monsoon winds blowing in the opposite direction from December to May. The holdover period between the two monsoon seasons proved ample time for merchants and missionaries to transplant customs, religion, and art from India to new environs in Southeast Asia. At the same time, the arrival of boats and merchants traveling from Vietnam and Malaysia to China and back as early as 300 BCE meant residents of Southeast Asia enjoyed a rich marketplace of ideas, goods, and cultures at a very early stage in world history.
While the influx of foreign ideas was critical to the development of societies across Southeast Asia, each local community made selective adaptations and preserved its indigenous customs. For example, the importance of the individual family was a point of commonality for many societies in Southeast Asia, in contrast to the weight given extended families and clan s in India and China. Most peasant communities in Southeast Asia also afforded women higher status than their counterparts in China were allowed under the stricter Confucian values system.
Archaeological remains of the region’s prehistory show that inhabitants of northeast Thailand used bronze and mastered agriculture as early as 3000 BCE. Evidence found at Non Nok Tha shows that they grew rice and cast bronze in factories using molds, later producing iron objects. The spread of rice cultivation produced densely populated centers along the region’s smaller fertile plains. Expanding populations were often forced into hilly regions, which they made suitable for farming by creating terraces. Migration chains and artifacts such as simple tools suggest that by the time the inhabitants of India began making contact with Southeast Asia, the islands and coastline settlements there were dominated by peoples related to Malays , who had made their way from southern China . Expert sailors working with finished stone tools and navigating by the stars, these peoples developed long, narrow boats that navigated Southeast Asia’s water with speed and grace. Moreover, they left behind cultures with maritime traditions that echo today with Malaysians, Indonesians, and the people of Singapore.
The archaeological record of Southeast Asia’s prehistory is less clear than that of many other areas of the world, however, and its study has been hampered by many circumstances, including the political volatility of countries such as Vietnam and Cambodia after 1945. As a result, historians often look to the region’s villages and families for insights into its remote past. For example, cultivating rice in terraced rice paddies requires skill and cooperation among many families, likely making this task the basis for village leadership and unity. Elders with experience in selecting breeds, transplanting young plants, and negotiating water resources likely used their authority to foster consensus around values and politics oriented toward giving deference to seniority. It is also possible that growing rice is particularly suited to cultures with animist religions, which venerate deities and spirits thought to inhabit nature. Rites and festivals to honor grains and timber and to appease forces that control wind and rain are still important to local cultures in Southeast Asia today, even as many people also participate in universal religions such as Buddhism .
Occupations offer another important point of continuity. Fishing, farming, and craftwork in fabrics are depicted in carvings found in caves, temples, and mountainsides and remain the primary labor activities of rural peoples today. For example, in Brunei many people still live much of their life on the water—at work as fishers and divers as well as at play when racing boats and swimming. Houses and many other buildings are still situated in the hills or on stilts to protect them from flooding, and many people share a diet of fish, simple grains, and coconut, just as their ancestors did.
In early Southeast Asia, trade and the arrival of outside religion were critical to the development of larger states and powerful kingdoms. Even in the interior, Buddhist artwork and texts flowed in steadily from 300 to 600 CE. The mouths of great rivers linked the interiors and the coasts, and capitals and small principalities that developed there taxed the trade on goods traveling to and from the wider world. During these centuries, Southeast Asians also traveled to India to trade and learn Sanskrit . When Indian elites and literate Buddhists arrived, they came to be known as purohita , advisers to Southeast Asia’s powerful chiefs and nobility. Other immigrants became teachers and founded temples across the region’s landscape, critical hubs that promoted travel, learning, and commerce.
As they did in India, Buddhism and Hinduism coexisted with local religions in much of Southeast Asia. In areas such as the kingdom of Srivijaya , which ruled over the island of Sumatra and southern Malaya Peninsula from the seventh to the twelfth centuries CE, Indian merchants and missionaries were welcomed, while the people retained their own religious traditions rooted in the worship of spirits that inhabited trees, rocks, water, and various physical features of the land. Proclaiming themselves “Lord of the Mountains,” Srivijaya’s rulers patronized Buddhism to foster trade relations across the Malaccan Straits and Indian Ocean.
Other communities, such as nearby Borobudur , which controlled central Java in Indonesia, were more firmly devoted to Buddhism. There, Buddhism inspired countless converts and the later Shailendra Kings (775–860 CE) to erect the world’s largest Buddhist monument, a structure more than one hundred feet above the ground and adorned with magnificent artwork (Figure 5.18). Buddhists from all over Southeast Asia made pilgrimages to Borobudur, leaving behind thousands of clay tablets and pots as offerings. Wreckage from a nearby ship dated to the ninth century shows that the people of Borobudur were engaged in commerce that connected them to Islamic and Arabic cultures in the Middle East. Like many heads of Southeast Asian states, Borobudur rulers staked their political legitimacy on setting a pious example for their subjects and thrived economically by opening their ports to the wider world. Thus India’s centrality to much of Southeast Asia in the ancient world was founded on trade, religion, and art. India was a repository of desired goods and a source of inspiration for religion and state-building, but also a bridge to the wider Eurasian world.
While much of Southeast Asia faced west toward India as the center of trade, culture, and religion, the area near today’s Vietnam fell within the orbit of China’s cultural sphere emanating from the east. The natural geography of Vietnam creates three distinct zones that shaped the evolution of the country from ancient times to the present: one area in the north surrounding the Red River delta; below that, in the south, another densely populated center on the Mekong River delta; and lastly, a long narrow land bridge along the coast squeezing between mountains to join the other two areas together. Humans practicing wet-field rice agriculture developed settlements in the northern zone sometime around 2500 BCE, and a millennium after, there is evidence of bronze-making by the region’s inhabitants. But the most notable contribution to world history from this area in northern Vietnam came from the Dong Son culture (c. 600 BCE–200 CE), defined by its remarkable bronze drums decorated with cords and images of animals such as frogs. Dong Son drums have been found at sites all over Southeast Asia.
Whether the Dong Son culture and its drums originated in Vietnam or inside China near Yunnan province is the subject of debate. Evidence suggests that southeast China below the Yangtze River was once home to peoples who were more strongly linked, culturally and linguistically, to Southeast Asia than to the dynasties in the north such as the Shang and Zhou. During the Zhou dynasty, many non-Chinese societies and kingdoms inhabiting provinces such as Fujian and Yunnan were known as the Yue , the Mandarin version of “Viet.” These areas and groups remained independent of Chinese control for centuries. Chinese records of the Yue demonstrate their sophistication and diversity. They were known for practicing wet-field rice cultivation, adorning their bodies with tattoos, and traveling widely by boat along the seas and the Red River that linked China to Vietnam .
These Chinese records further indicate that many early Vietnamese groups spoke a multitude of languages and were divided into as many as one hundred small polities, kingdoms, tribal clans, and autonomous villages. Unlike in northern China, there appears to have been no successful drive to centralize power under a unified dynasty in Vietnam’s prehistory. In later centuries, many Vietnamese accepted the mythological lore of a mighty king known as Van-Lang , who in the seventh century BCE united the various tribes of the Yue and established a dynastic line of Hung kings. This origin tale eventually evolved to include a divine origin for the Vietnamese people, telling of a union between a dragon lord and a female mountain deity that produced the Hung royalty.
At best, Vietnam’s prehistoric record can only validate the idea that chiefdoms grew increasingly large around 258 BCE. By then, the rulers of a new kingdom known as Au Lac had constructed an impressive capital arranged in the shape of a widening spiral near today’s Hanoi. Later, around 179 BCE, Au Lac was conquered by another kingdom, Nam Viet , an offshoot of China’s Qin dynasty. The area was later retaken by the Han dynasty, which attempted to establish permanent control by dividing its territory spanning southern China and northern Vietnam into nine administrative units. In 40 CE, Han control of the Red River delta ran afoul of two rebellious daughters of a Vietnamese general known as Trung Trac and Trung Nhi . The uprising launched by these women rallied native resistance from southern China to central Vietnam (Figure 5.19). Briefly victorious, the Trung sisters’ rebellion was eventually squashed. Their legacy was indelible, however, and stories of their exploits riding elephants into battle became a source of Vietnamese nationalist pride and rejection of encroachment by outsiders such as the Chinese and, much later, the French.
The end of the Trung sisters’ uprising began a period of more direct Chinese governance, with the aim of assimilating the region and its inhabitants. Over time, however, the families of the Han generals and officials who were sent as administrators took on many local habits and customs, blurring the boundaries between Chinese and Vietnamese culture in the ancient world. By that time, the area around the Red River delta had become critical to the Han’s maritime trade in Southeast Asia . Thus, even after the dynasty collapsed, China ’s political dominance of northern Vietnam lasted into the next few centuries. Sporadic uprisings continued, occasionally resulting in independence for rulers in northern Vietnam. But the Sui and Tang relaunched campaigns to reabsorb the Red River delta. Thus, northern Vietnam remained on the border of the Chinese imperial frontier for centuries.
Farther south, an area known in the ancient world as Champa was settled by a wave of people arriving from the sea around 500 BCE. Distinct from the Dong Son culture, these people engaged in trade across the waterways of Asia, from India to the Philippines. Chinese records of a civilization in this central region of Vietnam describe a unique people who reserved a higher status for women than for men, and who used an Indian script written on leaves from trees. Indeed, all the remaining inscriptions on artifacts found within this region until the ninth century are written in Sanskrit .
Another import from India to central Vietnam was the idea of a society led by a priestly Brahman class and deities such as Shiva , identified with the Champa kings. Still, indigenous spirits and ancestors were worshipped as well, coexisting alongside the Indian imports whose foreignness faded slowly over the centuries. Lacking a large agricultural region to supply a powerful state, Champa may have been a region with many centers, loosely knit by trading networks exchanging rice, salt, horns, and sandalwood.
Even farther to the south, people known as the Khmers had made the Mekong River delta their home by the early centuries of the common era. Chinese texts referring to this region named it Funan , and its history shows many similarities to that of Champa, its neighbor to the north. Funan too was engaged in wide trade. Archaeological remains show items that made their way to Vietnam from India, the Middle East, and Rome. Funan’s inhabitants and rulers imported features of Indian culture such as Sanskrit to help create royal courts, but little writing survived until the development of the powerful Khmer empire in the ninth century.


5: Gases
In this chapter, we examine the relationships between gas temperature, pressure, amount, and volume. We will study a simple theoretical model and use it to analyze the experimental behavior of gases. The results of these analyses will show us the limitations of the theory and how to improve on it.
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- 5.1: Gas Pressure
- Gases exert pressure, which is force per unit area. The pressure of a gas may be expressed in the SI unit of pascal or kilopascal, as well as in many other units including torr, atmosphere, and bar. Atmospheric pressure is measured using a barometer; other gas pressures can be measured using one of several types of manometers.
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- 5.2: Relating Pressure, Volume, Amount, and Temperature - The Ideal Gas Law
- The behavior of gases can be described by several laws based on experimental observations of their properties. including Amontons’s law, Charles’s law, Boyle’s law and Avogadro’s law. These laws can be extracted directly from the ideal gas law.
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- 5.3: Stoichiometry of Gaseous Substances, Mixtures, and Reactions
- The ideal gas law can be used to derive a number of convenient equations relating directly measured quantities to properties of interest for gaseous substances and mixtures. Appropriate rearrangement of the ideal gas equation may be made to permit the calculation of gas densities and molar masses. Dalton’s law of partial pressures may be used to relate measured gas pressures for gaseous mixtures to their compositions.
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- 5.4: Effusion and Diffusion of Gases
- Gaseous atoms and molecules move freely and randomly through space. Diffusion is the process whereby gaseous atoms and molecules are transferred from regions of relatively high concentration to regions of relatively low concentration. Effusion is a similar process with gaseous species passing from a container to vacuum through a small orifices. The rates of effusion of gases are inversely proportional to the square roots of their densities or to the square roots of their atoms/molecules’ masses.
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- 5.5: The Kinetic-Molecular Theory
- The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average velocities determined by their absolute temperatures. The individual molecules of a gas exhibit a range of velocities.
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- 5.6: Non-Ideal Gas Behavior
- Gas molecules possess a finite volume and experience forces of attraction for one another. Consequently, gas behavior is not necessarily described well by the ideal gas law. Under conditions of low pressure and high temperature, these factors are negligible, the ideal gas equation is an accurate description of gas behavior, and the gas is said to exhibit ideal behavior. The van der Waals equation is a modified version of the ideal gas law that can be used to account for the non-ideal behavior.
Contributors and Attributions
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).
- Thumbnail: As long as black-body radiation (not shown) doesn't escape a system, atoms in thermal agitation undergo essentially elastic collisions. On average, two atoms rebound from each other with the same kinetic energy as before a collision. Five atoms are colored red so their paths of motion are easier to see. (Public Domain; Greg L via Wikipedia )


7.2: Acid and Base Strength
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Objectives
After completing this section, you should be able to
- write the expression for the K a of a weak acid.
- convert a given K a value into a p K a value, and vice versa .
- arrange a series of acids in order of increasing or decreasing strength, given their K a or p K a values.
- arrange a series of bases in order of increasing or decreasing strength, given the K a or p K a values of their conjugate acids.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- acidity constant, K a
- equilibrium constant, K eq
Study Notes
Calculations and expressions involving K a and p K a were covered in detail in your first-year general chemistry course. Note that acidity constant is also known as the acid dissociation constant.
You are no doubt aware that some acids are stronger than others. Sulfuric acid is strong enough to be used as a drain cleaner, as it will rapidly dissolve clogs of hair and other organic material.
Not surprisingly, concentrated sulfuric acid will also cause painful burns if it touches your skin, and permanent damage if it gets in your eyes (there’s a good reason for those safety goggles you wear in chemistry lab!).  Water, which we know can act as a proton donor, is obviously not a very strong acid. Even hydroxide ion could theoretically act as an acid – it has, after all, a proton to donate – but this is not a reaction that we would normally consider to be relevant in anything but the most extreme conditions.
The relative acidity of different compounds or functional groups – in other words, their relative capacity to donate a proton to a common base under identical conditions – is quantified by a number called the acid dissociation constant , abbreviated K a . The common base chosen for comparison is water.
We will consider acetic acid as our first example. When a small amount of acetic acid is added to water, a proton-transfer event (acid-base reaction) occurs to some extent.
Notice the phrase ‘to some extent’ – this reaction does not run to completion, with all of the acetic acid converted to acetate, its conjugate base. Rather, a dynamic equilibrium is reached, with proton transfer going in both directions (thus the two-way arrows) and finite concentrations of all four species in play. The nature of this equilibrium situation, as you recall from General Chemistry, is expressed by an equilibrium constant , K.
The equilibrium constant is actually a ratio of activities (represented by the symbol \(a\)), but activities are rarely used in courses other than analytical or physical chemistry. To simplify the discussion for general chemistry and organic chemistry courses, the activities of all of the solutes are replaced with molarities, and the activity of the solvent (usually water) is defined as having the value of 1.
In our example, we added a small amount of acetic acid to a large amount of water: water is the solvent for this reaction. Therefore, in the course of the reaction, the concentration of water changes very little, and the water can be treated as a pure solvent, which is always assigned an activity of 1. The acetic acid, acetate ion and hydronium ion are all solutes, and so their activities are approximated with molarities. The acid dissociation constant, or K a , for acetic acid is therefore defined as:
\[ K_{eq} = \dfrac{a_{CH_3COO^-}·a_{H_3O^+}}{a_{CH_3COOH}·a_{H_2O}} ≈ \dfrac{[CH_3COO^-][H_3O^+]}{[CH_3COOH][1]} \nonumber \]
Because dividing by 1 does not change the value of the constant, the "1" is usually not written, and K a is written as:
\[ K_{eq} = K_{a} = \dfrac{[CH_3COO^-][H_3O^+]}{[CH_3COOH]} = 1.75 \times 10^{-5} \nonumber \]
In more general terms, the dissociation constant for a given acid is expressed as:
\[ K_a = \dfrac{[A^-][H_3O^+]}{[HA]} \label{First} \]
or
\[ K_a = \dfrac{[A][H_3O^+]}{[HA^+]} \label{Second} \]
Equation \(\ref{First}\) applies to a neutral acid such as like HCl or acetic acid, while Equation \(\ref{Second}\) applies to a cationic acid like ammonium (NH 4 + ).
The value of K a = 1.75 x 10 -5 for acetic acid is very small - this means that very little dissociation actually takes place, and there is much more acetic acid in solution at equilibrium than there is acetate ion. Acetic acid is a relatively weak acid, at least when compared to sulfuric acid (K a = 10 9 ) or hydrochloric acid (K a = 10 7 ), both of which undergo essentially complete dissociation in water.
A number like 1.75 x 10 - 5 is not very easy either to say or to remember. Chemists often use pK a values as a more convenient term to express relative acidity. pK a is related to K a by the following equation
\[pK_a = -\log K_a \nonumber \]
Doing the math, we find that the pK a of acetic acid is 4.8. The use of pK a values allows us to express the acidity of common compounds and functional groups on a numerical scale of about –10 (very strong acid) to 50 (not acidic at all). Table \(\PageIndex{1}\) at the end of the text lists exact or approximate pK a values for different types of protons that you are likely to encounter in your study of organic and biological chemistry. Looking at Table \(\PageIndex{1}\), you see that the pK a of carboxylic acids are in the 4-5 range, the pK a of sulfuric acid is –10, and the pK a of water is 14 . Alkenes and alkanes, which are not acidic at all, have pK a values above 30. The lower the pK a value, the stronger the acid.
Table \(\PageIndex{1}\): Representative acid constants
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protonated ketone pK a ~ −7 |
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phosphate monoester pK a ~ 1 |
phosphate diester pK a ~ 1.5 |
phosphoric acid pK a 2.2 |
protonated aniline pK a ~ 4.6 |
carboxylic acid pK a ~ 4-5 |
|
pyridinium pK a 5.3 |
carbonic acid pK a 6.4 |
hydrogen cyanide pK a ~ 9.2 |
ammonium pK a 9.2 |
phenol pK a 9.9 |
|
thiol pK a ~ 10-11 |
water pK a 14.00 |
amide pK a ~ 17 |
alcohol pK a ~ 16-18 |
alpha-proton pK a ~ 18-20 |
|
terminal alkyne pK a ~ 25 |
terminal alkene pK a ~ 35 |
ammonia pK a ~ 35 |
It is important to realize that pK a is not the same thing as pH: pK a is an inherent property of a compound or functional group, while pH is the measure of the hydronium ion concentration in a particular aqueous solution:
\[pH = -\log [H_3O^+] \nonumber \]
Any particular acid will always have the same pK a (assuming that we are talking about an aqueous solution at room temperature) but different aqueous solutions of the acid could have different pH values, depending on how much acid is added to how much water.
Our table of pK a values will also allow us to compare the strengths of different bases by comparing the pK a values of their conjugate acids. The key idea to remember is this: the stronger the conjugate acid, the weaker the conjugate base . Sulfuric acid is the strongest acid on our list with a pK a value of –10, so HSO 4 - is the weakest conjugate base. You can see that hydroxide ion is a stronger base than ammonia (NH 3 ), because ammonium (NH 4 + , pK a = 9.2) is a stronger acid than water (pK a = 14.00).
The stronger the conjugate acid, the weaker the conjugate base.
While Table \(\PageIndex{1}\) provides the pK a values of only a limited number of compounds, it can be very useful as a starting point for estimating the acidity or basicity of just about any organic molecule. Here is where your familiarity with organic functional groups will come in very handy. What, for example, is the pK a of cyclohexanol? It is not on the table, but as it is an alcohol it is probably somewhere near that of ethanol (pK a = 16). Likewise, we can use Table \(\PageIndex{1}\) to predict that para-hydroxyphenyl acetaldehyde, an intermediate compound in the biosynthesis of morphine, has a pK a in the neighborhood of 10, close to that of our reference compound, phenol.
Notice in this example that we need to evaluate the potential acidity at four different locations on the molecule.
pK
a
H
a
~ 10
pK
a
H
b
= not on table (not acidic)
pK
a
H
c
~ 19
pK
a
H
d
= not on table (not acidic)
Aldehyde and aromatic protons are not at all acidic (pK a values are above 40 – not on our table). The two protons on the carbon next to the carbonyl are slightly acidic, with pK a values around 19-20 according to the table. The most acidic proton is on the phenol group, so if the compound were to be reacted with a single molar equivalent of strong base, this is the proton that would be donated first.
As you continue your study of organic chemistry, it will be a very good idea to commit to memory the approximate pK a ranges of some important functional groups, including water, alcohols, phenols, ammonium, thiols, phosphates, carboxylic acids and carbons next to carbonyl groups (so-called a-carbons). These are the groups that you are most likely to see acting as acids or bases in biological organic reactions.
A word of caution: when using the pK a table , be absolutely sure that you are considering the correct conjugate acid/base pair. If you are asked to say something about the basicity of ammonia (NH 3 ) compared to that of ethoxide ion (CH 3 CH 2 O - ), for example, the relevant pK a values to consider are 9.2 (the pK a of ammonium ion) and 16 (the pK a of ethanol). From these numbers, you know that ethoxide is the stronger base. Do not make the mistake of using the pK a value of 38: this is the pK a of ammonia acting as an acid , and tells you how basic the NH 2 - ion is (very basic!)
Example \(\PageIndex{1}\): Acidic Groups
Using the pK a table, estimate pK a values for the most acidic group on the compounds below, and draw the structure of the conjugate base that results when this group donates a proton. Use the pKa table above and/or from the Reference Tables .
- Answer
-
a. The most acidic group is the protonated amine, pKa ~ 5-9
b. Alpha proton by the C=O group, pKa ~ 18-20
c. Thiol, pKa ~ 10
d. Carboxylic acid, pKa ~ 5
e. Carboxylic acid, pKa ~ 5
Example \(\PageIndex{2}\)
Acetic acid (CH 3 COOH) is known to have a pK a of 4.76. Please determine the Ka for acetic acid.
Solution
Solving for K a algebraically you get the following:
pK a = -Log(K a )
-pK a = Log(K a )
10 -pK a = K a
Using a calculator first enter in the value for the pK a (4.76). The make the number negative (-4.76). Next, use the inverse log function. All calculators are slightly different so this function may appear as: ANTILOG, INV LOG, or 10 X . Often it is the second function of the LOG button.
K a for acetic acid = 10 -pK a = 1.74 x 10 -5
Exercises
- Write down an expression for the acidity constant of acetic acid, CH 3 COOH.
- The p K a of acetic acid is 4.72; calculate its K a .
- The K a of benzoic acid is 6.5 × 10 −5 ; determine its p K a .
- From your answers to the questions above, determine whether acetic acid or benzoic acid is stronger
Answers
- \(K_a = \dfrac{[CH_3CO_2^-][H^+]}{[CH_3CO_2H]} \) or \(K_a = \dfrac{[CH_3CO_2^-][H_3O^+]}{[CH_3CO_2H]}\)
- \(pK_a =− \log_{10} K_a =4.74\)
- \(pK_a =−\log_{10} K_a =− \log_{10} 6.5 \times 10^{−5} =−(−4.19) =4.19\)
- Benzoic acid is stronger than acetic acid. [Benzoic acid has a higher K a and a lower p K a .]


3.1: Biblical Insight
Applying the Bible to Business
In this chapter, we will be looking at different leadership styles. The Bible provides insight into how to be a great leader. In Matthew 20:26, Jesus teaches us how to be great in the Kingdom of God: “ Whoever wants to become great among you must be your servant.” Matthew 20:26.
In a world of self-promotion, Matthew 20:26 takes a different approach to accomplishing greatness. A servant leader focuses primarily on the empowerment and supporting the well-being of others. Traditional leadership styles generally involve a “top-down” approach to employees. In other words, the influence of position and authority is used over employees. The servant-leaders take a different approach to working with employees. A servant leader will put others first and promote employees to meet their highest potential.
When we apply this biblical insight to business, we can see that it supports the leadership style called “servant leadership.” Take a moment to consider how a "servant leader" can impact employees and business profits. If you want to be a great leader, consider how you can practically be a "servant leader" right now. What things can you implement in your daily life to focus on being a servant leader?


1.4: Checking Values
At the end of this section you should be able to answer the following questions:
- Is level of measurement for variables a consideration in checking for out of range responses?
- Is the scale of the variables a consideration in checking for out of range responses?
One of the first steps in understanding one’s data is to check the values across the cases for indications the responses are what you would expect to see. These expectations should be based on the level of measurement and the scale of the variables.
Therefore, one of the most important data checks you would initially undertake is making sure all of the responses for each variable indicate a value within a range of appropriate values. This is known as checking for out-of-range responses .
For example, if you asked participants to write down their age in years, and you find a person who has responded with 512, there is a good chance this was an error made by the participant. Another example would be if you are asking people to rate how happy they are on a 1 to 5 scale, and you get a response of 8. This is another obvious error. These types of responses can occur when a person isn’t paying attention to what they are typing or if there is a coding error in the survey software.
If you have found an obvious error in a person’s demographic information, there isn’t much you can do about it. You can remove that data point, or the whole case, depending on the circumstance. However, if there is an incorrect response in a 1 to 5 scale, you could use mean replacement to correct the inappropriate response.


16.2: The Coulomb force
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Coulomb was the first to provide a detailed quantitative description of the force between charged objects. Nowadays, we use the (derived) SI unit of “Coulomb” (C) to represent charge. The “charge” of an object corresponds to the net excess (or lack) of electrons on the object. An electron has a charge of \(-e=-1.6\times 10^{-19}\text{C}\) . Thus, an object with a charge of \(-1\text{C}\) has an excess of about \(-1.6\times 10^{19}\) electrons on it, which is a very large charge. If an object has an excess of electrons, it is negatively charged and we indicate this with a negative sign on the charge of the object. An object with a (positive) charge of \(1\text{C}\) thus has a deficit of \(-1.6\times 10^{19}\) electrons.
Through careful studies of the force between two charged spheres, Coulomb observed 1 that:
- The force is attractive if the objects have opposite charges and repulsive if the objects have the same charge.
- The force is inversely proportional to the squared distance between spheres.
- The force is larger if the charges involved are larger.
This leads to Coulomb’s Law for the electric force (or simply “Coulomb’s Law”), \(\vec F_{12}\) , exerted on a point charge \(Q_1\) by another point charge \(Q_2\) :
\[\vec F_{12}=k\frac{Q_{1}Q_{2}}{r^{2}}\hat r_{21}\]
where \(\hat r_{21}\) is the unit vector from \(Q_2\) to \(Q_1\) and \(r\) is the distance between the two charges, as illustrated in Figure \(\PageIndex{1}\). \(k=8.99\times 10^{9}\text{N}\cdot\text{m}^{2}\text{/C}^{2}\) is simply a proportionality constant (“Coulomb’s constant”) to ensure that the quantity on the right will have units of Newtons when all other quantities are in S.I. units. In some instances, it is more convenient to use the “permittivity of free space”, \(\epsilon_0\) , rather than Coulomb’s constant, in which case Coulomb’s Law has the form:
\[\begin{aligned} \vec F_{12}=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r^2}\hat r_{21}\end{aligned}\]
where \(\epsilon_{0}=\frac{1}{4\pi k}=8.85\times 10^{-12}\text{C}^{2}\cdot\text{N}^{-1}\cdot\text{m}^{-2}\) is a more fundamental constant, as we will see in later chapters.
If the two charges have positions \(\vec r_1\) and \(\vec r_2\) , respectively, then the vector \(\hat r_{21}\) is given by:
\[\begin{aligned} \hat r_{21} = \frac{\vec r_2 - \vec r_1}{||\vec r_2 - \vec r_1||}\end{aligned}\]
Coulomb’s Law is mathematically identical to the gravitational force in Newton’s Universal Theory of Gravity. Rather than quantity of mass determining the strength of the gravitational force, it is the quantity of charge that determines the strength of the electric force. The only major difference is that gravity is always attractive, whereas the Coulomb force can be repulsive.
Exercise \(\PageIndex{1}\)
The Coulomb force is conservative.
- True.
- False.
- Answer
- A.
The product \(Q_1Q_2\) in the numerator of Coulomb’s force is positive if the two charges have the same sign (both positive or both negative) and negative if the charges have opposite signs. Again, referring to Figure \(\PageIndex{1}\), if the two charges are positive, the force on \(Q_1\) will point in the same direction as \(\hat r_{21}\) (since all of the scalars are positive in Coulomb’s Law) and thus be repulsive. If, instead, the two charges have opposite signs, the product \(Q_1Q_2\) will be negative and the force vector on \(Q_1\) will point in the opposite direction from \(\hat r_{21}\) and the force is attractive.
Example \(\PageIndex{1}\)
Calculate the magnitude of the electric force between the electron and the proton in a hydrogen atom and compare this to the gravitational force between them.
Solution
We model this by assuming that the electron and proton are point charges a distance of \(1 \unicode{xC5}=1\times 10^{-10}\text{m}\) apart (\(1\) Angstrom is about the size of the hydrogen atom). The proton and electron have the same charge with magnitude \(e=1.6\times 10^{-19}\text{C}\) , so the (attractive) electric force between them has a magnitude of:
\[\begin{aligned} F^{e}=k\frac{Q_{1}Q_{2}}{r^{2}}=(9\times 10^{9}\text{N}\cdot \text{m}^{2}\text{/C}^{2})\frac{(1.6\times 10^{-19}\text{C})(1.6\times 10^{-19}\text{C})}{(1\times 10^{-10}\text{m})^{2}}=2.3\times 10^{-8}\text{N} \end{aligned}\]
which is a small number, but acting on a very small mass. In comparison, the force of gravity between an electron ( \(m_e=9.1\times 10^{-31}\text{kg}\) ) and a proton ( \(m_p=1.7\times 10^{-27}\text{kg}\) ) is given by:
\[\begin{aligned} F^{g}=G\frac{m_{2}m_{p}}{r^{2}}=(6.7\times 10^{-11}\text{Nm}^{2}\text{/kg}^{2}\frac{(9.1\times 10^{-31}\text{kg})(1.7\times 10^{-27}\text{kg})}{(1\times 10^{-10}\text{m})^{2}}=1.04\times 10^{-47}\text{N} \end{aligned}\]
Discussion
As we can see, the electric force between an electron and a proton is \(39\) orders of magnitude larger than the gravitational force! This shows that the gravitational force is extremely weak on the scale of particles and has essentially no effect in particle physics. Indeed, the best current theory of particle physics, and the most precisely tested theory in physics, the “Standard Model”, does not need to include gravity in order to provide a spectacularly precise description of particles. One of the big challenges in theoretical physics is nonetheless to develop a theory that integrates the gravitational force with the other forces.
Example \(\PageIndex{2}\)
Three charges, \(Q_1=1\text{nC}\) , \(Q_2=-2\text{nC}\) , and \(q=-1\text{nC}\) , are held fixed at the three corners of an equilateral triangle with sides of length \(a=1\text{cm}\) , with a coordinate system as shown in Figure \(\PageIndex{2}\). What is the electric force vector on charge \(q\) ? (Note that \(1\text{nC}=1\times 10^{-9}\text{C}\) ).
Solution
The net electric force on charge \(q\) will be the vector sum of the forces from charges \(Q_1\) and \(Q_2\) . We thus need to determine the force vectors on \(q\) from each charge using Coulomb’s Law, and then add those two vectors to obtain the net force on \(q\) . The force vectors exerted on \(q\) from each charge are illustrated in Figure \(\PageIndex{3}\).
The force from charge \(Q_1\) has magnitude:
\[\begin{aligned} F_{q1}= \left|k\frac{Q_{1}q}{a^{2}} \right|=(9\times 10^{9}\text{N}\cdot\text{M}^{2}\text{/C}^{2})\frac{(1\times 10^{-9}\text{C})(1\times 10^{-9}\text{C})}{(0.01\text{m})^{2}}=9\times 10^{-5}\text{N} \end{aligned}\]
and components:
\[\begin{aligned} \vec F_{q1}&=-F_{q1}\cos(60^{\circ})\hat x-F_{q1}\sin(60^{\circ})\hat y\\[4pt] &=-(4.5\times 10^{-5}\text{N})\hat x-(7.8\times 10^{-5}\text{N})\hat y\end{aligned}\]
Similarly, the force on \(q\) from \(Q_2\) has magnitude:
\[\begin{aligned} F_{q2}=\left |k\frac{Q_2q}{a^2}\right |=(9\times 10^{9}\text{N}\cdot \text{m}^2\text{/C}^{2})\frac{(2\times 10^{-9}\text{C})(1\times 10^{-9}\text{C})}{(0.01\text{m})^2}=1.8\times 10^{-4}\text{N}\end{aligned}\]
and components:
\[\begin{aligned} \vec F_{q2}&=-F_{q2}\cos(60^{\circ})\hat x+F_{q2}\sin(60^{\circ})\hat y\\[4pt] &=-(9.0\times 10^{-5}\text{N})\hat x+(1.6\times 10^{-4}\text{N})\hat y\end{aligned}\]
Finally, we can add the two force vectors together to obtain the net force on \(q\) :
\[\begin{aligned} \vec F^{net}&=\vec F_{q1}+\vec F_{q2}\\[4pt] &=-(4.5\times 10^{-5}\text{N})\hat x-(7.8\times 10^{-5}\text{N})\hat y-(9.0\times 10^{-5}\text{N})\hat x+(1.6\times 10^{-4}\text{N})\hat y\\[4pt] &=-(13.5\times 10^{-5}\text{N})\hat x+(8.2\times 10^{-5}\text{N})\hat y\end{aligned}\]
which has a magnitude of \(15.8\times 10^{-5}\text{N}\) .
Discussion
In this example, we determined the net force on a charge by making use of the superposition principle; namely, that we can treat the forces exerted on \(q\) by \(Q_1\) and \(Q_2\) independently, without needing to consider the fact that \(Q_1\) and \(Q_2\) exert forces on each other.
Footnotes
1. Others had initially observed the inverse square law for the electric force, but Coulomb was the first to formalize the theory.